Chairperson, Graduate Committee: Nicolas Yunes and Neil J. Cornish (co-chair)Moore, Blake CarrollTravis Robson, Nicholas Loutrel and Nicolas Yunes were co-authors of the article, 'A Fourier domain waveform for non-spinning binaries with arbitrary eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.Nicholas Loutrel was a co-author of the article, 'A 3PN Fourier domain waveform for non-spinning binaries with moderate eccentricity' in the journal 'Classical and quantum gravity' which is contained within this dissertation.Nicolas Yunes was a co-author of the article, 'Data analysis implications of moderately eccentric gravitational waves' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.Nicolas Yunes was a co-author of the article, 'Constraining gravity with eccentric gravitational waves: projected upper bounds and model selection' submitted to the journal 'Classical and quantum gravity' which is contained within this dissertation.2021-04-052021-04-052020https://scholarworks.montana.edu/handle/1/15899The ground based advanced Laser Interferometer Gravitational wave Observatory (LIGO) has now made numerous detections of compact objects, ushering in an era of gravitational wave astronomy. Soon the Laser Interferometer Space Antenna (LISA) will become operational and allow for even more detections of gravitational waves. With these detections we are able to characterize the physical properties of the sources - the nature of the orbit, the parameters of the individual compact object, and the parameters of the final merged object. Beyond these source measurements, gravitational waves have proven an important test bed for validating General Relativity, as well as testing theoretical astrophysical formation scenarios of these compact binaries. In order to reach these ends, we require accurate and efficient models for the gravitational waves as seen in the detector. While current detections by ground based detectors are consistent with compact binaries in quasi-circular orbits, there are formation scenarios which suggest that some small number of detectable events will be from compact objects in eccentric orbits, and certainly a healthy number of sources detectable by LISA will be in eccentric orbits. We have derived, validated, and explored the data analysis properties of a waveform model for compact objects in eccentric orbits. In the derivation of the waveform we have employed a truncated sum of harmonics, the stationary phase approximation, and a bivariate expansion in eccentricity and orbital velocity. To explore the data analysis implications of this model we have implemented Markov Chain Monte Carlo algorithms to produce the posterior distributions on the waveform parameters. We find that our model is highly accurate for the inspiral phase of compact objects in orbits with eccentricity as high as 0.8, and very computationally efficient - taking only 90ms to evaluate on average. System parameters are best measured when the source eccentricity is about 0.4, sometimes providing two orders of magnitude better measurement than its quasi-circular counterpart, and eccentric signals can provide more stringent constraints on alternative theories of gravity.enGravitational wavesGeneral relativity (Physics)Quantitative researchMultiple starsDissertationCopyright 2020 by Blake Carroll Moore